Unit

Modulatíon Basie De inition

rNanow bor.
modulation:
Frequeny Lwide band
FM
Tionsmission bondwidth
FM spnals
qeneration FM signals

tation o FM
Demodu
fM stereo Multplexing
Modulation-’ clt) is vaned
Angle
Defiotion process the angleamplitude valuesf
in ohch
the nstantaneous
It is the constant.
accordance withampitude o c(t) modulation
io
nt), Keeping the Angle
tso types 4 Modulation
FscquenayModulation
9
Phase
Modulation’
equensy m)

cH)
+ The iequencs oq cmmie caye chage la accoatirg t
mesage signal
+ 1# is a tom angle modulatíon n which instar!,
Yiequency. l) 6 vayíe Iineasly wrth mt) s gien b

tiequenyg tquen!. mo du lating

un modutatedSensitivity signa
cayics tafuolt
tlt): dt

de
side, o t
dt
on both
Jote gyating
O()
mt))
fan (t, + ky

elt)
ancet + ankm) dt >
be ositten as,
domaio Can
wGVe in time
* AM
st)A, cos[ot)] -
Sub 4 in 5

3(t) Ac
An Cos anfmt
.. mt) tr
ankAm Cosanttdt
Ac cos antt +
3t) 9ntmt
ah k sin
cos anct +
- A
deviatfon
 odulafon index AtM
wheie

tco type
Nanouw Bond TM
Wide Band IM
J

Ssiort tor FM is
domaín expe (ontmt) ’0
The
time.
an t +pSin
A cos[
s4):
tsing tignonmetrie identity
COSB- Sin ASioA
(A+B) = CosA Sin anfmt
Cos B: B
Qnfet : -sin (onj.t)
A sinanfmt) sin(p sínant-nt)
(arnyet) (p
cos
S4): Alcos appyoxímate
to
is possible
Small, henceit
BiS
n NBFM, coslp sin antm)
sinlp sinanft)
sinankct (g
"
(arrget) - Ac anfmt ’9
S): A,cosaT14ct- BAcSin amfctsin
S). AcCos cos (A4B)
cOs(A-B) -
WkT
+BA cosllk
BAe cosan(4 mt
Stt) A, cosar}et-
..
wave Consists ot
he fM freguency' H
amplitude A
3 caien uoith amplitude Ac requeneytct bm
353 ith
 LSB with amplitude BAc with tequeny
i,
b The narow band fM eqtuic s Sorne band oid
that e AN
Fouyfen tansfom on both sides q eyn s
Taking

Nanow Band FM is
hansissipo Banduidth
* 4S)

AcF

AcP

Total po Lt Ap°

is Same, pooer s ao
+ Wheneve, magnitude of spechum
agnrtude but not an
ame as it deperds enly

Wide Band FM-’

It hay a much lar ge Volue B. which s theont
-ally inite
 For larg ualue B.the F wove ideolly cortains the
cami & an inkinite ne side bands tocated Symmctrícally
axound the caie Bandidth and hence calle A
FM wave has infini te
k Such a
wide band FM guen by
sinusoidal modulaton is
EN wave tor Dt+ p sin anfmt)
O
slt) A cos
anfet psin anmt
s(t) RT Ac e psinamgmt)]
i(antet +
SA)= Re Ac Jantet

Re[ eJanket,
ReLesanget, s'te) ’
st)S4) AeBSinaD7mt trequency,
tundamental
Whese tuncton with a
is a periodie tme
s) Sesies as,
complex ouvies
be expressed usingCn Janntmt
+ This Can
Co-e}feient gfven by
complex touria
lahere Cn -jannbmt dt
s'u)e

Sub 3 in 5 get
dt
Ae e

anmt - nnmt]
Jlpsin
Ac tm

anfmt ’
let itpoigas
/Afm
 dt
dt :
dx
anhm
the tinmits

anfmt
WkT when t
-I
ohen t:
afm atm

Jlpsin-na)
artm
Actm
ilpsinn-nn) da
Ac- tm

ilpsinn-n)
dz
Ae

Ac
0(psín - n)
where, ,nth sideswith an
a t kind
bessel tunction
To (B) Ga
t
in janntrt
Sub eyn 8
Stt)
jannmt jantet]
Sub 9 in a
st). Re Ac
 SL4):

Coso jsíne an (je +nfm)!

Cose

Similaay cos(anlGetntn)t
Jnlg)
s(): A,
n, betwcen- to to
Values tor to t o
the
42, - a,
i·e, n: 0, l, -,
(fetfm)t + I,(p) Cosanls
+J(p) Cos an + a (a)
cos[an(fe-abn
(fetafm)t)+J,(p)[an(te-3tm)t) ’
+ 3,()cos(an3tm)t)+J.z (p)cos
cos[anCte+
an(fetatm)t -
S(t) = (fe-afmt+ 34p)[cos
(jetafnt-cosan
+5( cosan Component &an
inkinite
has a cariz
Thus modulated Signa taym tet 3fm, te t ntm
frequencies tefm,te
number side sides ¢ egn u we get,
torer transtorm on both
Taking

fsl-(4e-nf)+
&(F+(fetnhm}+A Jn
f-Ge+nt)+
the Spectaum the above coua tion
As Jo(p)
No plotting

tet fm ttam
 Eandwidth FM
lhon smission side band6, So th.
no
FM has infinite is aso ntintte.
Theouitfcalty to tharnsmission
bondwidth 2equied
oidthtormula tor an F4
genenolized the Eond
Cosson ppoximate tormula tor computin,
to bim, the a geneated by a Single ton
Acéouding
the band uadth an FM Signal m' is
ncy
modulating signal reque
B tor all values ¢ 'B:
tormula holds good also be ex peSsed :
the above bandi dth 'B can
transmision
* The deviatfon '4'.
terms 4 trequeny
A
tm

From can O.

tm

Compaision FM& AM ’
AM
wove is
wave is tan toY AM
tos FM anhet
Egn
st) Acup cosan7mt)cos
stt) Ariagnftpsihan
can . Modulatfion îndex is alunys
a. Modulation index in beteen
value ie.,
have an
 3. Thonsmitted pouer is conie , ne stde hand
at u6eless
powen
A
tuo Side tonds
5 Jn AM,
6

de
-the modulation index
tesmines the no g
side ye produced,
modulatfon index onpecfue
bands in an FM Signal B. hm
Bw alA +tm) BN doesnt depend
an modula modulation Yndex
Banduidth depend
-tíon in dex index Am,
/. modul ation
4 modulahon index=
Actuat teg deviation
allowed treg devíation ceptible to
may more Sus
FA oves AM 8 AM is noist
8- Advantage noise moc eHected by
is the
noise immunity thon FM
Qre ess
9 AM quipmerts
tansmission and vecep
9- FM cornplex
-tion ea uipment
complex AM transmission s cheopey
Io
b FM transmis sion s erpens than EM
-(Ne tthan AM
Wsed tor long distance
t Used tor
short distance I1:
communication.
Communieaton
qengation IM Sarals->
essertally too basit nethods agrenating
+ There ase
trequency modulated oves
parametey Vaniaton method
| Dizect FM 6i) metho
FM (oa) Armstrong
J. In diect
paametey viotion method);
| Direct Method (
this method, the instantaneous trear o the
+ Jn
to the modulatng
carrie wave is orie d according shnal by
Aeice called a bltage- Conbolled oscillator (ue
wse a circuit that convexts
* To produce FM, We
ito a corresponding chang n capacitarce indu
votag
to the oscllatu tank.
the FM is obtained by the
* Here, o» parameter
Maniation any element
depends s called
on uhich the tre method" o FM
Parametey Vaiation -e4)

genenatton the ttartley oscilator is

oscilation
* The tea o
by. ti lt)

tuoo inductance total capacit ante fked capacit

in tuned circuit vaiable voltoge capacto
wave, mt) the capocrtance ct) is given b
+ For mnoul at ing
ct) vaiabe capocito Sensitis
toto! capacitonce to wdtoge chang
in absence o modulotion
Sub

ar J(tlco(

ascillation
Unmodulated trea d

tl4)
tilt) ot ky m)
device Called a Wottage. conti olled oxilator (veo
moduce fM, We ue a cíhcut thot converts a
toge
etag into a coneponding chang fn capaitarce )ina ,
to the scllat tank
+ Here, the FM is
obtained by he
Vaniation any element o panameter
On hich 4he treq depends
is called
vaníaton method" o FM
Par amete
qenenation esalatr is al
ascilation a the ttartley
+ The tea, o
by b )

oo inductance k total capacit ance tixed capact

in tuned circuit vaiable volttage capacto
capacrtance c) is gien
+ For modulat ing wave, mt) the
-k-nt) ’
Lvoia be capocitoa Sensit
totat capadtante to vdtage chang
modulation
in absence d
Sub

l)

an J(Ltl)co (t-Kmit))
Co

tilt) Co
ascillation
Unmoduated te o
t0

to nmt-G)
tlt) to + kymt)
 where kË to k 6A the Tesultant eg sensitvity
d the modutat
has an dísadvantage, that camien eq
4 the direct mehod highly Stable oscillator
tDm a method, here
s not obtained stabilization stable
OUeIcome this oe use treqoscillator which is vay mixo
k To, gentiated by a cystal gneratos is applied to a
conier is the odp 4 FM
Io this method,
cnystal ascilator. to frea díscrj
& q applied
olp ditterence freg tesm & freqy g the FM
uth the
along products the proportional to the
Mixes voltage
produce s olp Then tor
-minatos, t a LPF
applied to its ilpdisaiminator is applied to devia
aue trea iS tero freguency
olp o LPF
* The freg, the olp proportional tocasics
treguency Anditis
Corect carier voltage carier
de olp
assigned value the
gies
Ittrom the
*-tion oscillator
moditytreg
VCo to
applied to Frequency
stab'lied FM
mtt) bltage
odulotng Contsolle
modute Oscillato6
slgn Contso!
vottag
Ampities
coTIect
signal mixe
kystal
oScilatos
Freay
disciminato
LPF <
(Avnstong method):achieved by
Method is
2 Indisect Amstrong method
geheaten usingGenevation of PM wave PM wave
+ FM a Genexotion NBFM
from
BFM1om NBFM
foliowing Steps:
6 Genexotiono

Pm wave?
Generaton o
phae modulato
PM
 Csaato is ued to generate a stable
* Gysta
unrnodul
Cavier ohich s applicd to 90° phase shi<ten ç-the summing c
Balanced
atea
e phase sh ted coier is applicd to the
* The signat. Thus the, shi{ted carex
atong wlth the modulating
in the balanced moduBator guing us ony te
modul ated
DSBSC
fo phase orth q0° shited ca
bands with thei tesultart are
side bands the unshited cariex
* The too the yesutant Vectos addition o
Sumning cicuit to get
bands
Caraiex tuoo side
modulotg Balanced DSBSC+ 90° Summing PM
modulato Cir cuut
CDSBSc)

)
96 phase
shitted
caune

phase shitt
Coien
csystal
osllatoy
uSB

Suppsessed
Canne
o'ghitted
Casrler () LSB
Carricn Resutant
side bands
important to note that i the
usBReultant * It s Tesultant carsie,
sdebads
phase shit the
phast
exceeds 36 then along oith
we hove amplitude modulaton- Th.
moduBa tion,
Aistortion
Tepesents
Reeping the phae shift wrthin limits [l
* By is obtained.
Reualtart puse phoase modulation
at olp
4 Surm
ckt
 6) GenevatiÍn NBIM fxem FM:
modulating tegato
phase o NOF M
modulatos

cxpressicn tor a PM wove, unt]’0

-the +mp Sín
st): Ae cos[wt
let s(4) : Ae coS
where e s t 4 mp Sin umt
angulay frequercy the PM oave s defied
+ Instantancous
u; do:dut +n, Sin unt)
dt dt

|41 te + mp tm cosLÛmt
trequency deviation
ABmay mptm
medulatng votage, the
the
Snce mp is proportfonal to with the modulatng oitage
otl ay in proportion
tequeney ti obtained using PM
thus FM can be om NBFM:
WBFM signal first
) Generation modulatíng
Jhdirect method FM, thetreg devíation is increased
+h thexctore the s Conested b
genexates NBEM E the NBFM
NBEM into WBFM.
by converting trequency multiplicas
NBFM by usfng
tolt) NBFM Frequeny WBFM
jennato multiplic FM Lyave
S, block diaqtam generato
NBFM Non-linean BPF WBFM
dovíce
maltiplicn
 multfple contafns,t
taeq uency
nti devio
wava ith caniex {requency
na s wad:
on-linean devfce caiea
The BPF 4oleuingave eentered at
the
FM
pass the
deviation na semainíng fM Spectro.
with rq all
completely
i, To atteruate tve,: vecovered fucm the t.
Detection 4 FM trg signal ís
origina) modula
* The Balanced slope detec ty
Disect me thod
díscyiminatu t )
6) Fequeny detecto oster seeley
b) Zero- cossing
discoimirob
(os)
disaiminatoy
c) Phase de tector
d) Radio
Indiect method
loop detector-
Phase- locked
) Balanced slope
discsíminator (o)
Fequeny
D

R Vo
Vo
f M ve

SIt)
signad

detectoa consists
V

Balanced slope
* The detectos cireusts
two slope has a centse
trans formey
Hence the ilp
topped secondany slape detectors
tages to the too
vol phase
aye I80° out tuned Civcuits
+ Therc
are 3 v£nge
IF iie., tr
The pimary is tuned to
 they o olp principle
tnedtuned detetovs the ip the +veisVo tin 'T'.-Ve in-ve
lie,
taking the diviaing caies
but
idertical 'e' "'. în Hene is the is
s (h)i than voltage,than detecto
(7,) A slope in
induced " on waVe
scondevy by Voz
serondory than higher ates
" tuo citained by to equal ates D,
is Yo wi ndin g
nding be
gre dp less slop
Balanced
the operFM
itteythe voltages
tequenty
civcuits
tfon
cpen is
requency
bothalso
the than Thus is tht winding
'7'
in
an
the the uill is hghey strequency than tor
q is
vologea the hencetrequency
ov
Vo ilp
uohen thon
Dg detecotrequency
q Mo the :tollews
as Vo1 Da) higher
o
chcut cirouitesonant olp
voltage untenstand the in -tovolt a
&ges is hi g (¢
her
individuo ilp ced Mo
Voltages ondíng detecto
csossirg
tuned the p when
fintei-
ih
Vol B age
fndu polepposi
oritites, Voz ilp uoltisage instanto
is olp when Ddiode,
d
tune
pen lowes
ts
ie,, the olp
ax tnal
the
Cpexotionrongts
:tino thatip
induced olpthe D, -e
" to mduced
the qeter
Vo'
than voltag
ol
Ttehe ronge
ney
teque
.'.o
crossng
tero
the n
.The
cane4
equat
to Thusde in ip the to
he
Ne -nce -y Jbe The voltoghe thon voltag he
the
# 4 +
 4i
ohere
time ditevence beteen adjacent eso Cioss
At is the
the FM Ove

k
AAA
T
in accordance oth
' is chosen
he tirme intenval
tolleuwing too conditions e
is smal compaued to the ecipsocal
J, the nterval '
w'ie,
message Banduuf dth compatcd to the epIoCal t.
the interval ' s large wave, ie, te
Ü, e the FM
eaien freaq,uency
denote the number d
zer erossings foside the
+ let 'no
the time
betueen the odjocernt
ence, at is
-val T'
csossing points given by.
At :

Instantancous treguency fs giern by

Qx

no

hstantaneous }requency, wktthe

the denition
between ti mess age signa mlt) ene,
is a ineay elation n S knouon:
con secover m(t)
Baae Band
imitey fPulse Irtegrate
geneatone
M
Jnput ied
when phase e)
be the LpF
can FM, a by athrough
It detor ectos iliter
teedthetrequencydetection (vco)
system
back
led
contro
output
’
ts: esci
Componenl atos
phase pass
beCan
vco
oscillationdpasse
low
the is
tos contaol ed a
as
the Ued porsbast Seving iswhich Loopftes
fpliey
-ve the mul
sinal
i
çphasencomi ng ctrequency
veo votage
a mainly thsce
mul
A
&.
isjatio voltage tiplietltes, the
is
PLL the has omparatoTnput
lbop r a
n ip q
The track isIt
noise PL A he voltaitsge clp
to- :
A with The
an * 3 + +
(lte, 4 tten appied to the p the vto his volt age
veo q keeps the loop n lor
ehanges the trequency the
Condition
Jtoop
Muove 4lte
)

veok controlled by the extenal voll.

Veo an be Navíes linearly worthits np
e equency freguency
ascillation
In a vco, the e)loop t
tnougha LPF
passed Thís voltage then changes
voltag the multiplies 5 Vco.
* The olpappied to the ilp d the the toop in locked cond'i
¬then
trequency the Veo keeps
the
FM s ) Loop
wave
1ltes

then Vco is adjuty

voltage to Vco
is.zero,
nitially, the contol
* equal to the unm
So that, made
the VCo is exactly
treaueny
-ulated caie trequency "te ° wt the unmodalated
shit
VCo op has a phase
Q. The
carsies wave
the PL is given by
The p to [atct + 0, lt)] -’0
st) Ae Sin have
uoth a modulating sgnal mtt), oe
,t) ak+ m)dt ’
Vco, then
the olp
IL () denotes 4(1))’
[antet+ voltage to Veo
Vt)- Ay cos voltage applied as ip
the contol
I Vt) is t

then
teq sensitivity vco
st) & the vco ol rlt) are the ton
wave,
t The incorming N
 e's to miiple he clp et) &
gven by

sinA coSAsin (A18) +solA B

The LPF dp is given by

elt): km Ae Ay sin| 4l)- d,(] ->0
elt) Kon Ae Avy Sin ( te6]
hihere, ) is the phase trro
. ) ,(t)- 0t

The loop filter operates on ts ip, e() to produe the clp,

e(t) h(t-t) dt ’@O
cohere ht) is the impulse esporse titer.
Sub l in l0, then

disbexentiating eqn 1a uowt ime we get,

dt)
dt

dat) ako sin .to] h(t-) dt ’

dt t
by
nhere ko ís loop paamete iven 5)
ken ky Ae Av
ko
Non-lineoan model PLL
produces non- lineas model. Thís model includes the
+ tn th
9¬13.
belationshin botueeo Vt) elt) as vepresente dby eyn